Pauling’s Rules

Studio portrait of Linus Pauling. 1930.

Studio portrait of Linus Pauling. 1930.

“I am enclosing a copy of a manuscript which Mr. Sturdivant and I have prepared, dealing with the structure of brookite. We feel rather confident in our structure, and are pleased to have begun work in the field which you recently opened — the study of complex ionic crystals.”

– Linus Pauling. Letter to William Lawrence Bragg. May 31, 1928.

X-ray diffraction, as discovered by Max Theodore Felix von Laue, is the process of examining a crystalline substance by tracking the scattering of x-rays upon contact with a given material. The process goes something like this: An x-ray photograph is taken, releasing x-rays which then interact with the sample and subsequently interfere with one another. This interference results in an image, known as a Laue photograph, of a diffraction pattern in which the x-rays that have passed through the crystal appear as small black dots. A trained crystallographer can then use this photograph as the basis for deriving the molecular structure of the sample crystal.

In the late 1920s, x-ray diffraction appeared to have reached the peak of its usefulness. Crystallographers had pinpointed the structure of most simple, few-atom crystals and were left to struggle with increasingly complex molecules. Unfortunately, with the addition of only one or two atoms, a crystal’s structure became considerably more difficult to derive. In complex molecules, the diffraction patterns were much more intricate, allowing for a large number of theoretically possible structures. Crystallographers, with the help of their lab assistants, were forced to wade through pages of complex mathematics in search of the correct structure. Pauling and J. Holmes Sturdivant, who were working together on complex crystals, had taken to hiring teams of students to crunch the calculations necessary for this sort of approach.

Pauling was dissatisfied with this process and felt that there had to be another way to attack the problem. He noted that many researchers involved in the field had discovered similar molecular structures and bonding patterns between different crystals, which suggested a limited number of structural possibilities. With this in mind, Pauling believed it possible to develop a guide which would help researchers derive molecular structures of complex crystals via the x-ray diffraction technique.

Supplementing his knowledge of crystalline structures and quantum mechanics with existing research, Pauling attacked the problem. In a short time, he was able to develop five simple guidelines for eliminating scores of theoretical structures, thereby greatly reducing the difficulty of solving molecular structures.

Pauling’s Rules, first published in 1928 as a part of his paper “The Principles Determining the Structure of Complex Ionic Crystals,” are still considered valid by today’s scientific community. They are as follows:

1. A coordinated polyhedron of anions is formed about each cation, the cation-anion distance is determined by the sum of ionic radii and the coordination number (C.N.) by the radius ratio.

2. An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an anion equal the charge on that anion.

3. The sharing of edges and particularly faces by two anion polyhedra decreases the stability of an ionic structure.

4. In a crystal containing different cations, those of high valency and small coordination number tend not to share polyhedron elements with one another.

5. The number of essentially different kinds of constituents in a crystal tends to be small.

After developing these rules, Pauling began to apply them in his own research. In 1929 and 1930, he worked at solving the structures of groups of silicates, including but not limited to mica and talc. Using his new system of rules, as well as an x-ray powder diffraction apparatus that he had built, Pauling was able to decipher previously unknown bonding patterns. His work with zeolites, for example, uncovered the basis of their unique gas-absorption properties, a problem that had baffled many of his contemporaries.

Pauling’s Rules propelled the young researcher to the forefront of the crystallographic community. In a very short time, he had become a major player in a reputable branch of structural science. Moreover, his use of both the crystallographic and quantum mechanical disciplines hinted at a possible meshing of the fields unlike anything seen before. The young scientist was well on his way to international fame on a grand scale.

Learn more about Pauling’s Rules on the website “Linus Pauling and the Nature of the Chemical Bond: A Documentary History.”